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Function: Domain and Range

A function is a correspondence between two sets governed by some rule(s) such that each member of the first set corresponds to exactly one member of the second set. The first set is called the domain of the function. The second set is called the range of the function.

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Function: Domain and Range

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  1. A function is a correspondence between two sets governed by some rule(s) such that each member of the first set corresponds to exactly one member of the second set. The first set is called the domain of the function.The second set is called the range of the function. In this course the members of each set are real numbers. For now, x will represent a real number from the domain and y or f (x) will represent a real number from the range. Function: Domain and Range Recall the definition of a function. The following slides deal with identifying domain or range from various function representations.

  2. Function: Identifying the Domain and Range Example 1 (Function represented by a set of ordered pairs.) State the domain and range of the function: { (- 1, 2), (3, 5), (6, 5) }. The domain is { - 1, 3, 6 }, because each first set (domain) member is represented by x (the left slot in each ordered pair. The range is { 2, 5 }because each second set (range) member is represented by y (the second slot in each ordered pair. Slide 2

  3. Example 2: State the domain of Recall from the definition (slide 1) that each member of the domain must correspond to exactly one member of the range. Here, any number we choose to replace for x will result in exactly one value for y, except for x = 3. This value for x does not correspond to a value for y, since, is not defined. Therefore, the domain is all real numbers except 3 or (- , 3)  (3, ). Function: Identifying the Domain from an Equation Slide 3

  4. Example 3: State the domain of Recall from the definition (slide 1) that each member of the domain must correspond to exactly one member (a real number) of the range. Here, only values of x that are - 3 or larger will correspond to a real number for y. For example, if x = - 7, which is not a real number. One way to quickly find the domain is to set the radicand of an even index radical  0 and solve. Here, x + 3  0, so the domain is x - 3 or [- 3, ). Function: Identifying the Domain from an Equation Slide 4

  5. Example 4: State the domain and range of the function shown graphed. Function: Identifying the Domain and Range from a Graph Note that points on the graph have x-coordinate values that span from - 4 to 4. Since each domain member is represented by x, the domain is [ - 4, 4 ]. Note that points on the graph have y-coordinate values that span from 0 to 5. Since each range member is represented by y, the range is [ 0, 5 ]. Slide 5

  6. Function END OF PRESENTATION Click to rerun the slideshow.

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